Deep learned 2D quadrilateral finite elements

Abstract

In this work, we propose a method that employs deep learning, an artificial intelligence technique, to generate stiffness matrices of finite elements. The first proposed method is to generate a stiffness matrix by training the strain from the reference data model. The elements generated using the first method practically pass the patch tests and the zero energy mode tests. The second proposed method is to generate a stiffness matrix through an analytical strain and setting the local coordinates using deep learning. The elements generated using the second method pass the patch test and zero energy mode test. Through various numerical examples, the performance of the developed elements is investigated and compared with those of existing elements. It was confirmed that the deep learned finite elements can potentially outperform existing finite elements.